Question

Factor the polynomial expression 16y^4-256x^12

Answer 1

Answer:

Step-by-step explanation:

4y^2+16x^6, 2y, 4x^3, 2y, 4x^3

Answer 2

Answer:

see explanation

Step-by-step explanation:

Given

16$y^{4}$ - 256$x^{12}$ ← factor out 16 from each term

= 16($y^{4}$ - 16$x^{12}$ ) ← difference of squares which factors in general as

a² - b² = (a - b)(a + b), thus

$y^{4}$ - 16$x^{12}$

= (y² )² - (4$x^{6}$ )²

= (y² - 4$x^{6}$ )(y² + 4$x^{6}$ )

Now y² - 4$x^{6}$ ← is also a difference of squares

= y² - (2x³)²

= (y - 2x³)(y + 2x³)

Thus

16$y^{4}$ - 256$x^{12}$

= 16(y - 2x³)(y + 2x³)(y² + 4$x^{6}$ )